Two identical steel spheres

PHYSICS · Multi-part · CBSE · Physics · Work, Energy and Power · Work, Energy and Power

Problem

Two identical steel spheres, each of mass

0.25\,\text{kg}

, collide on a nearly frictionless horizontal surface. The laboratory technician conducts three separate trials and records the speeds of each sphere immediately before and immediately after each collision, as shown in the table. Trial Data (positive speed values are to the right; negative to the left)

Trial	$u_1$ (m\,s $^{-1}$ )	$u_2$ (m\,s $^{-1}$ )	$v_1$ (m\,s $^{-1}$ )	$v_2$ (m\,s $^{-1}$ )
1	$+1.2$	$0.0$	$+0.4$	$+0.9$
2	$+1.0$	$-0.50$	$-0.20$	$+1.1$
3	$+1.3$	$0.0$	$+0.6$	$+1.4$

Here,

u_1

and

u_2

are the initial speeds of Spheres 1 and 2, respectively, and

v_1

and

v_2

are their speeds immediately after the collision in the same trial. Neglect energy losses to the surface. (a) For each trial, calculate the total kinetic energy of the two-sphere system just before and just after the collision. (b) For each trial, state the percentage change in total kinetic energy and classify the collision as elastic, inelastic, or perfectly inelastic. If the data do not permit a physically valid classification, indicate why. (c) One of the trials appears to violate energy conservation based on your calculations. Propose at least one plausible experimental factor that could produce such an apparent increase in kinetic energy.

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